A man borrowed some money from a private organization at 5% simple interest per annum. He lent this money to another person at 10% compound interest per annum and made a profit of Rs.26410 in 4 years. The man borrowed:
Answer & explanation
Correct answer: option 4
The profit earned by man of Rs. 26410 is the difference between CI and SI of 4 years.
Let the sum is P.
So, CI of 4 years = P(1 + \(\frac{10}{100}\))4 - P
= P [ (\(\frac{11}{10}\))4 - 1]
= P [ \(\frac{14641}{10,000}\) - 1]
= \(\frac{4641P}{10000}\)
SI of 4 years = P × \(\frac{5}{100}\) × 4
= \(\frac{20P}{100}\)
Now,
CI - SI = \(\frac{4641P}{10000}\) - \(\frac{20P}{100}\)
⇒ [\(\frac{4641-2000}{10000}\)]P = 26410
⇒ \(\frac{2641P}{10000}\) = 26410
⇒ P = 10,00,00